If you read this blog, then you probably already know about xkcd, the web comic by the geektastic Randall Munroe. What you may not know is that Randall really is just that smart, with a keen interest in physics and math. He likes thinking about big-picture stuff, including taking what might seem like silly ideas and running with them to see where they lead.

So I’m really excited to see he’s started a blog called "what if?" He takes crazy questions from readers and answers them, following the logic wherever it may lead.

The inaugural post asked, what if you threw a baseball at very nearly the speed of light? I have seriously thought about this as well, and while I found myself smiling at Randall’s explanation – his thinking followed mine very closely – he took a turn I hadn’t thought about: atoms in the air undergoing nuclear fusion with the baseball. Huh.

The second post, which just went up, is about how well you’d score if you answered SAT questions randomly, and somehow due to Randall’s machinations all the US Presidents and 75% of the the cast of Firefly get electrocuted by lightning.

Huh.

As usual, this is clever, funny, odd, and just plain cool. You’ll feel smarter – you’ll be smarter – after reading it.

Comments (61)

Blaise Pascal

The xkcd forum has further discussion of the baseball question. Several people make the observation that at 0.9C the kinetic energy of the baseball is greater than the nuclear binding energy of it’s particles, so Randall’s wrong about the fusion — you’ll get nuclear spallation instead.

There is also an absolutely hilarious “Mythbusters” parody embedded in the comments as well.

I particularly like the comment on the baseball one: “A careful reading of official Major League Baseball Rule 6.08(b) suggests that in this situation, the batter would be considered “hit by pitch”, and would be eligible to advance to first base.“

Actually, the atoms hitting the ball would probably NOT fuse. The velocity of 0.9C is way, way too hot for the comparatively vaster lower energies involved in fusion reactions. The nuclei would likely be converted into a plasma of nucleons. The protons won’t do anything, and the neutrons would have to cool way down before they did anything.

As Dutch Railroader’s comment demonstrates, there is a fair bit of controversy over whether there would actually be fusion. At that speed, the particles in the baseball may not be able to hold together long enough to fuse.

IANAPhysicist, but I suspect there could be secondary fusion reactions in the vicinity nevertheless. Maybe the baseball and the surrounding air gets turned into a plasma of elementary particles, but perhaps other parts of the stadium would undergo fusion? I’m not sure…

Hum – this is interesting, especially when you compare it to Dr. Asimov’s short story “The Billiard Ball”. Then again, in Dr. Asimov’s story, the cue ball is moving at an infinitesimal fraction less than the speed of light, not a a mere 90% of C.

A baseball is usually 32-36 ounce, roughly 1kg.
At 0.9c, total kinetic energy is roughly 25MT, so, pretty much on par with a large nuclear device. There is surely enough energy to cause the damage outlined, but how quickly the energy of the ball is dumped into the environment, I am less sure.

Overall, I am skeptical and I don’t feel I am smarter after reading it, on the contrary, I feel more anxious to read more comment to find out whether other people agree with Randall or not.

The energy you have to play with is 4M-ton, but there’s no confinement, compression, or good fusion fuel. The XKCD analysis is correct that it would have the kinetic and thermal effects of an equivalent nuke, but the nuclear component would be trivial…

So now we could look up pp / pn / nn cross sections at this energy… any ideas what would happen? In practice, there will be enough ‘grazing’ collisions where whole nuclei interact coherently, and do fuse, as Randall says.

I am a chemistry student and admittedly did not pay THAT much attention to relativity in my physics courses… but should there not be some length distortion of that ball? And how does that work if there is some degree of rotation (as would be expected from a normal pitch)?

The what if cartoon is interesting, but as usual the comments on it here are far more interesting and educational.

Here’s a question to those in the know here. If fusion is unlikely in this case, does it matter? If the ball were thrown at lower speed, whatever is optimal for fusion, would there be more destruction?

Also, at 0.9c would there be a “shell” or ring of fusion at some distance from the ball, or perhaps fusion taking place in the wake?

@19 Fusion is irrelevant in this case. With 0.9c you have 4MT to get rid of in a small area. Reducing the speed of the ball reduces the amount of energy correspondingly (using the proper relativistic expression for mass/energy of the ball). The basic issue is that N and O in the atmosphere and C,N,O,H in the ball are very low yield fusion fuels that are hard to light, and the geometric setup is completely incompatible with any sort of ignition (that is getting the fusion to feed itself). This is not to say that some fusion reactions would not occur (say in the cooler halo around the ball), but the energy release would be completely trivial by several orders of magnitude compared to the energy available directly by turning the ball into plasma…

at .9c would any of the matter involved in the collision be transformed into antimatter? and then would there not be a matter/antimatter incident that would probably make a “mere” fusion explosion look trivial?

Hm. Like many of the comments, I am not so sure there is enough confinement for fusion, but the 4MT kinetic energy of the ball would certainly make a huge bang.

What I want to know is whether the team can send in a replacement runner from their protected underground bunker. It seems unlikely that the original batter could ever be successfully reassembled on first base.

@21 No – you might have local temperatures right at the start sufficient to make electron/positron pairs at some low level, but that only turns one form of energy into another. Any way you might make antimatter requires energy consumption that would be only returned by annihilation. The only energy you have to play with is what the ball had to start with…

I think it’s also worth noting that all the radiation/explosions/fireworks etc will be highly boosted in the direction that the baseball was thrown.

So while a mushroom cloud might still form due to heat transport after the plasma is created – the X-Ray/gamma-ray front shouldn’t be spherically symmetric, it should almost all point away from the pitcher.

The baseball fan in me loves this (Go Rangers!) but I, too, am skeptical that fusion would happen in any sustained, confined sort of way. Nukes are precision devices and we are talking about spreading those reactions along a distance of 60’6″ from rubber to home plate. I’m no physics expert, and I know the Ivy Mike device was a few stories tall, but I don’t think that a sudden appearance of a HyperBaseball would make that kind of explosion from fusion alone.

This reminds me of a line from Joe Haldeman’s “The Forever War”, in a section discussing the after-effects of a kinetic energy weapon: “at that speed, it didn’t matter whether you’d been hit by a nova-bomb or a spitball. ”

What I’m wondering though, is really what the rate of energy transfer would be. It’s easy to say that the baseball has 4 MT of kinetic energy, but how much of that actually gets used before it punches through everything and leaves the atmosphere?

On the SAT one, I wish he had pointed out that the probability of getting all the answers correct is 1/2.7 x 10^110….JUST LIKE EVERY OTHER SPECIFIC OUTCOME!

Creationists are very fond of pointing out that the odds of arriving at the current configuration of life on earth by chance are extremely low. That’s true, as far as it goes. But in fact, it’s no less likely than any other outcome, and probably more likely than most.

Want to experience an extremely unlikely event yourself? Toss a coin 100 times, recording the outcome. You’ve just experienced a probablility of 1/2^100!

“What I’m wondering though, is really what the rate of energy transfer would be. It’s easy to say that the baseball has 4 MT of kinetic energy, but how much of that actually gets used before it punches through everything and leaves the atmosphere?”

Well, you’ve got 145g of baseball, which looks an awful lot like a 1cm thick, 40sq-cm area plate, with a nuclear x-sectional area ratio of 0.44, meeting 1Kg of nitrogen & oxygen nuclei every 2.5 meters.

I would expect, after the initial conversion to a gas of nucleons, their speed would drop rapidly with each collision, and they would be down to fusion energy speeds once the cloud has expanded roughly to a cube 100m a side.

So assuming the matter of the ball is blown outwards reasonably efficiently, you’ve got roughly 100m or so before it’s just an explosion.

I don’t know too much about physics, but I do know a bit about baseball. The paragraph referenced states that the batter is not entitled to take the base if he (or she *) makes no attempt to avoid being hit. At that speed, there’d be little time to duck.

* I have two daughters who played fast pitch softball – as a matter of fact, the whole scenario would be more plausible in softball since the pitchers can throw faster – angular rotation and all that.

The densities simply aren’t high enough for significant fusion, even if the ball were thrown more slowly. The Sun’s corona is hotter than its core by orders of magnitude, and yet no fusion occurs because the densities are far too low.

@ 5

Sure, there could be secondary fusion, but this would release on the order of MeVs per nucleus, while each nucleus has dozens of GeVs of pure kinetic energy to release. Any fusion would be irrelevant.

This actually raises an intriguing question for me – assuming otherwise current technology except in propulsion, would the ISM prevent 0.99c travel? If not, what altitude from the sun could you travel at 0.99c without being shredded by the solar wind / heliosphere?

And more interestingly, if the first question has a negative answer, what /would/ be a safe speed to travel at through the ISM?

The only one who could throw a ball that fast is Superman. If you threw it up ,it would escape the Earths gravity and go into space. Where as the frist law of motion says it will stay in motion keep going usless something efects it (something in its way or the gravational pull of some object) How about if someone hits the ball sending at near the speed of light for a homerun?

@Space Cadet Small nit to pick: pitchers in fastpitch softball do NOT throw faster than in baseball. It may appear that way bc the pitcher is MUCH closer to the batter than in baseball: 40 feet in h.s. and 43 feet in college. Thus in fastpitch softball the ball arrives at roughly the same time a good major league fastball would. This (and the underhand motion) is why major league hitters are so often embarrassed by going against top flight female softball pitchers. A good fastball in women’s softball may go around 70 mph while a REALLY good fastball in MLB can break 100 mph but even minor league pitchers routinely throw 92-95 mph.

A ball thrown by Superman into space at .9c would drastically effect the way the baseball moves through the different mediums such as air . . . etc. I think.
However what if gravity could impose such pressure on the atoms of the baseball that they would not deteriote or fuse with the elements in the air (all moving through the higgs) at what has already been mentioned. That first law of motion is going to encounter all types of effects and things in the way. Unless, possibly gravity and charge work together like king and quenn or because Superman is just that awesome.

That should be king and queen. And , personally I don’t know if the ball stands to disintegrate even on the atomic level directly out of Supermans hand, but Iam leaning that way. :-

Btw . . . whose side is Time on . ? . this close to the known ultimate speed limit: c . . . and how could Time thus collaborate with Gravity within the Higgs Field and the other forces of the Universe to hypothetically hold Supermans greatest pitch in one piece as a measurable mass for 1 second . ? . I doubt it as cool as it sounds mike burkhart
Superman will beat up any superhero . . . just wanted to add that

And if Superman were to throw a baseball that fast I think Superman himself would have to be moving close to c and just might obliterate some of the surrounding Earth with his wind up . . . Thus obliterating the baseball before it is ever to be thrown.

Iam pretty sure just on instinct here that at .9c for 1 second the baseball would be well into space given the ball could take the stressors.

That “What if” blog idea is pure, distilled awesome.
The only thing I’d add is the actual energy of the baseball in question, which I was immediately curious about. At first I couldn’t believe that even a relativistic fastball could wreak quite that much havoc, so I checked it out (thanks, Wolfram Alpha!) The kinetic energy of a 145 gram baseball traveling at .9 C is 1.69×10^16 joules, equal to just a hair over 4 megatons of TNT. That’s one helluva brushback!

@49 starsrift: This actually raises an intriguing question for me – assuming otherwise current technology except in propulsion, would the ISM prevent 0.99c travel? If not, what altitude from the sun could you travel at 0.99c without being shredded by the solar wind / heliosphere?
And more interestingly, if the first question has a negative answer, what /would/ be a safe speed to travel at through the ISM?

That is indeed an interesting question. The average density of the ISM is known, so I’m sure someone with more math acumen than I could throw together a back-of-the-envelope calculation to determine how much interstellar hydrogen you’d encounter per second, then get the relativistic kinetic energy of that mass at your chosen speed to get the energy flux your ship would be dealing with.
Alas, I suck at math, so someone else will have to do it